Ohm's law: the relationship between voltage, current and resistance, the meaning of resistance, and calculating the total resistance of resistors in series and in parallel.

What this key area is asking

The SQA wants you to use Ohm's law to link voltage, current and resistance, explain what resistance is, and calculate the total resistance of resistors combined in series and in parallel.

Ohm's law and resistance

Rearranging gives $I = \frac{V}{R}$ (more voltage or less resistance gives more current) and $R = \frac{V}{I}$ (used to find the resistance from measured voltage and current). For a resistor kept at a constant temperature, doubling the voltage doubles the current, so a $V$ against $I$ graph is a straight line through the origin whose gradient is the resistance.

Resistors in series

Resistors in parallel

The most common slip with the parallel rule is to forget to take the reciprocal at the very end: you find $\frac{1}{R_T}$ first and then flip it to get $R_T$.

Checking your answer

A quick sanity check saves marks: a series total must be larger than every resistor, and a parallel total must be smaller than every resistor. If a parallel answer comes out larger than one of the resistors, you have probably forgotten to take the reciprocal at the end.

It also helps to understand why the rules work. In series the current must pass through every resistor in turn, so each one adds its opposition and the total resistance grows. In parallel the current has a choice of paths, so adding another branch always makes it easier for charge to flow overall, which lowers the total resistance. A special case worth remembering is two equal resistors in parallel: the total is always exactly half of one of them, because the two paths share the current equally.

Ohmic and non-ohmic components

A component that obeys Ohm's law, giving a straight-line $V$-against-$I$ graph through the origin, is called ohmic; a fixed resistor at constant temperature is the usual example. Some components are non-ohmic: a filament lamp gets hotter as the current rises, so its resistance increases and its $V$-against-$I$ graph curves. At National 5 you should be able to recognise that a curved $V$-against-$I$ graph means the resistance is changing.

Try this

Q1. A $12 \text{ V}$ supply drives a current of $3.0 \text{ A}$ through a resistor. Calculate the resistance. [2 marks]

• Cue. $R = V/I = 12/3.0 = 4.0 \text{ }\Omega$.

Q2. Resistors of $5 \text{ }\Omega$ and $15 \text{ }\Omega$ are in series. Calculate the total resistance. [1 mark]

• Cue. $R_T = 5 + 15 = 20 \text{ }\Omega$.

Q3. Two $20 \text{ }\Omega$ resistors are in parallel. Calculate the total resistance. [2 marks]

• Cue. $\frac{1}{R_T} = \frac{1}{20} + \frac{1}{20} = \frac{2}{20}$, so $R_T = 10 \text{ }\Omega$.